Three-dimensional Magnetohydrodynamics Research Articles

Constraints on Acoustic Wave Energy Fluxes and Radiative Losses in the Solar Chromosphere from Non-LTE Inversions

Accurately assessing the balance between acoustic wave energy fluxes and radiative losses is critical for understanding how the solar chromosphere is thermally regulated. We investigate the energy balance in the chromosphere by comparing deposited acoustic flux and radiative losses under quiet and active solar conditions using non–local thermodynamic equilibrium inversions with the Stockholm Inversion Code. To achieve this, we utilize spectroscopic observations from the Interferometric BIdimensional Spectrometer in the Na i 5896 Å and Ca ii 8542 Å lines and from the Interface Region Imaging Spectrograph in the Mg ii h and k lines to self-consistently derive spatially resolved velocity power spectra and cooling rates across different heights in the atmosphere. Additionally, we use snapshots of a three-dimensional radiative magnetohydrodynamics simulation to investigate the systematic effects of the inversion approach, particularly the effect of attenuation on the velocity power spectra and the determination of the cooling rates. The results indicate that inversions potentially underestimate acoustic fluxes at all chromospheric heights while slightly overestimating the radiative losses when fitting these spectral lines. However, even after accounting for these biases, the ratio of acoustic flux to radiative losses remains below unity in most observed regions, particularly in the higher layers of the chromosphere. We also observe a correlation between the magnetic field inclination in the photosphere and radiative losses in the low chromosphere in plage, which is evidence that the field topology plays a role in the chromospheric losses.

Heat transport analysis of three-dimensional Magnetohydrodynamics nanofluid flow through an extending sheet with thermal radiation and heat source/sink

Regarding heat transformation efficiency, the hybrid nanofluid performs superior to the nanofluid. The majority of hybrid nanofluid uses are in the industrial sector, producing solar energy, cooling generators, and vehicle heat transformation. Heat transfer and nanofluid velocity are the two most crucial transport properties that must be evaluated before the first and second thermodynamics equations are applied to nanoscale fluids. The objective of this work is to investigate the characteristics of transmission of heat of magnetohydrodynamic (MHD) nanofluid (Ag/H2O)and hybrid nanofluid (Ag+Al2O3/H2O)flow on a linear extensible sheet when magnetic forces are present. Similarity variables are applied to transform a set of nonlinear dimensionless partial-differential equations to collection of ordinary-differential equations. The non-analytical solutions of these transformed equations are found utilizing the MATLAB mathematical program's bvp4c function. The impression of various physical attributes along skin friction coefficients and properties of heat transmission are analyzed. The behavior of key parameters, including surface stretching ratio, rotational and magnetic effects, for temperature and velocity, is shown using graphs and tables. In conclusion, hybrid nanofluids, which comprise silver and aluminum oxide nanoparticles dispersed in water, outperform silver-water nanofluids by around 10-15% under magnetohydrodynamic (MHD). The higher thermal conductivity of these hybrid nanofluids allows for better heat dissipation, making them an appealing option for applications that need optimal thermal management in the presence of magnetic fields.

Structure Formation Through Magnetohydrodynamical Instabilities in Primordial Disks

The shear flow instabilities under the presence of magnetic fields in the primordial disk can greatly facilitate the formation of density structures that serve as seeds prior to the onset of the gravitational Jeans instability. We evaluate the effects of the Parker, magnetorotational and kinematic dynamo instabilities by comparing the properties of these instabilities. We calculate the mass spectra of coagulated density structures by the above mechanism in the radial direction for an axisymmetric magnetohydrodynamic (MHD) torus equilibrium and power density profile models. Our local three-dimensional MHD simulation indicates that the coupling of the Parker and magnetorotational instability creates spiral arms and gas blobs in an accretion disk, reinforcing the theory and model. Such a mechanism for the early structure formation may be tested in a laboratory. The recent progress in experiments involving shear flows in rotating tokamak, field reversed configuration (FRC) and laser plasmas may become a key element to advance in nonlinear studies.

Exploring the Magnetic and Thermal Evolution of a Coronal Jet

Coronal jets are the captivating eruptions that are often found in the solar atmosphere and primarily formed due to magnetic reconnection. Despite their short-lived nature and lower energy compared to many other eruptive events, e.g., flares and coronal mass ejections, they play an important role in heating the corona and accelerating charged particles. However, their generation in the ambience of nonstandard flare regime is not fully understood, and warrant a deeper investigation, in terms of their onset, growth, eruption processes, and thermodynamic evolution. Toward this goal, this paper reports the results of a data-constrained three-dimensional magnetohydrodynamics (MHD) simulation of an eruptive jet; initialized with a non-force-free-field (NFFF) extrapolation and carried out in the spirit of implicit large eddy simulation (ILES). The simulation focuses on the magnetic and dynamical properties of the jet during its onset, and eruption phases, that occurred on 2015 February 5 in an active region NOAA AR12280, associated with a seemingly three-ribbon structure. In order to correlate its thermal evolution with computed energetics, the simulation results are compared with differential emission measurement analysis in the vicinity of the jet. Importantly, this combined approach provides an insight to the onset of reconnection in transients in terms of emission and the corresponding electric current profiles from MHD evolutions. The presented study captures the intricate topological dynamics, finds a close correspondence between the magnetic and thermal evolution in and around the jet location. Overall, it enriches the understanding of the thermal evolution due to MHD processes, which is one of the broader aspects to reveal the coronal heating problem.

Unveiling the Connection between the Alfvénic Oval and the Open–Closed Field Line Boundary at Ganymede

Alfvén waves generated by the interactions between the Ganymede magnetosphere and the fast-corotating Jovian plasma carry a significant amount of energy. This energy is partially transferred to precipitating particles, which correspond to a feature called the Alfvénic oval. However, the spatial distribution of the Alfvénic oval in the Ganymede system is unclear, and the physical correlation between the Alfvénic oval and the open–closed field line boundary (OCFB) has not been studied quantitatively. Using a high-resolution, three-dimensional global magnetohydrodynamics simulation of Ganymede's magnetosphere, we investigate the spatial distribution of the Alfvénic oval mapped on the ionosphere surface of Ganymede based on upstream measurements from Juno's PJ34 flyby. Our results show that (1) the simulated Alfvénic oval of Ganymede closely resembles the observed aurora oval, and although without kinetic physics, the magnitude of the simulated Afvénic Poynting flux is significantly lower than the estimation based on auroral luminosity; (2) the OCFB aligns closely with the poleward (equatorial) boundary of the enhanced Alfvénic power on the downstream (upstream) side; and (3) the magnetospheric flux tube convection pattern can guide the Alfvénic wave packet to propagate toward latitudes either equatorward or poleward of the OCFB on the downstream/upstream side. These results, presented for the first time in this study, provide testable predictions for both the ongoing Juno mission and future Jovian missions such as JUICE probing the minimagnetosphere system.

Application of three-dimensional MHD equilibrium calculation coupled with plasma response to island divertor experiments on J-TEXT

Three-dimensional (3D) equilibrium calculations, including the plasma rotation shielding effect to resonant magnetic perturbations (RMPs) produced by the island divertor (ID) coils, were carried out using the HINT and MARS-F codes on J-TEXT. Validation of 3D equilibrium calculations with experimental observations demonstrates that the shielding effect will prevent the penetration of the edge m/n = 3/1 mode component when the ID coil current is 4 kA, while change the size of magnetic islands once the current exceeds the penetration threshold. This indicates that equilibrium calculations including the plasma rotation shielding effect to RMPs can lead to better agreements with experimental observations compared to the vacuum approximation method. Additionally, the magnetic topology at the boundary undergoes changes, impacting the interaction between the plasma and the target plate. These results may be important in understanding RMP effects on edge transport and magnetohydrodynamic (MHD) instability control, as well as divertor heat and particle flux distribution control.

Numerical investigation of magnetic reconnection in Jupiter’s dayside magnetodisc

Dayside magnetodisc reconnection is a unique process that may occur in rapidly rotating magnetospheres with internal plasma sources, and it is not expected at Earth. Several observations suggest that dayside magnetodisc reconnection could be driven in the Kronian magnetosphere. This raises the question as to whether it can occur at Jupiter, the fastest rotating planet in the Solar System. Recent reports have suggested its occurrence, but the limited number of identified events leaves the overall global picture in the Jovian magnetosphere uncertain. The primary objective of this study is to answer whether dayside magnetodisc reconnection could exist within the Jovian magnetosphere through the use of global magnetohydrodynamics (MHD) simulations. Additionally, we aim to conduct a numerical investigation to reveal its general distribution for possible future exploration. The numerical simulations for Jovian magnetospheric dynamics are based on three-dimensional MHD calculations, which enable magnetic reconnection through numerical resistivity. In post-processing procedures, the simulated magnetodisc reconnection event is primarily identified by equatorial $B_ reversals, accompanied by an analysis of local plasma flows and global magnetic field lines. Our global MHD simulations reveal the existence of magnetodisc reconnection within the dayside Jovian magnetosphere. The simulation results indicate that dayside magnetodisc reconnection is more likely to occur during solar wind rarefaction, primarily due to the rapid expansion of the dayside magnetospheric volume. This expansion allows a rotation-driven centrifugal force to generate sufficient magnetic field line stretching for current sheet thinning and reconnection. In simulated dayside events, $B_ reversals may occur locally or non-locally through rotational transport from reconnection sites at earlier magnetic local times. The existence and the features derived from simulations are testable as Galileo/Juno has accumulated a considerable amount of dayside magnetospheric data. These results are valuable for future Jovian missions, such as JUICE and Europa Clipper, and provide new insights into interpreting measurements from other rapidly rotating systems.

General Relativistic Radiation Magnetohydrodynamics Simulations of Precessing Tilted Super-Eddington Disks

We perform a three-dimensional general relativistic radiation magnetohydrodynamics simulation of a tilted super-Eddington accretion disk around a spinning black hole (BH). The disk, which tilts and twists as it approaches the BH, precesses while maintaining its shape. The gas is mainly ejected around the rotation axis of the outer part of the disk rather than around the spin axis of the BH. The disk precession changes the ejection direction of the gas with time. The radiation energy is also released in approximately the same direction as the outflow, so the precession is expected to cause a quasiperiodic time variation of the observed luminosity. The timescale of the precession is about 10 s for a 10 M ⊙ BH and for the radial extent of a disk of several tens of gravitational radii, where M ⊙ is the solar mass. This timescale is consistent with the frequency of the low-frequency quasiperiodic oscillation (0.01–1 Hz) observed in some ultraluminous X-ray sources.

Magnetically Arrested Circumbinary Accretion Flows

Binary systems with comparable masses and a surrounding accretion disk can accrete gas through spiral accretion streams penetrating the central cavity formed by tidal interactions. Using three-dimensional Newtonian magnetohydrodynamics simulations, we investigate the possibility of a magnetically arrested accretion flow through the cavity. Rather than solely continuously feeding the binary through spiral accretion streams, the accretion is regulated by the strong magnetic field inside the cavity. Transport of mass and angular momentum onto the binary then proceeds largely periodically in magnetic flux eruption episodes. The ejected flux tubes carry angular momentum outward and away from the binary, inject hot plasma into the disk, and can launch flares. This likely intermittent scenario could have potential implications for the emission signatures of supermassive black hole binaries and shed light onto the role magnetic fields play in the binary’s orbital evolution.

A reduced ideal MHD system for nonlinear magnetic field turbulence in plasmas with approximate flux surfaces

This paper studies the nonlinear evolution of magnetic field turbulence in proximity of steady ideal Magnetohydrodynamics (MHD) configurations characterized by a small electric current, a small plasma flow, and approximate flux surfaces, a physical setting that is relevant for plasma confinement in stellarators. The aim is to gather insight on magnetic field dynamics, to elucidate accessibility and stability of three-dimensional MHD equilibria, as well as to formulate practical methods to compute them. Starting from the ideal MHD equations, a reduced dynamical system of two coupled nonlinear partial differential equations for the flux function and the angle variable associated with the Clebsch representation of the magnetic field is obtained. It is shown that under suitable boundary and gauge conditions such reduced system preserves magnetic energy, magnetic helicity, and total magnetic flux. The noncanonical Hamiltonian structure of the reduced system is identified, and used to show the nonlinear stability of steady solutions against perturbations involving only one Clebsch potential. The Hamiltonian structure is also applied to construct a dissipative dynamical system through the method of double brackets. This dissipative system enables the computation of MHD equilibria by minimizing energy until a critical point of the Hamiltonian is reached. Finally, an iterative scheme based on the alternate solution of the two steady equations in the reduced system is proposed as a further method to compute MHD equilibria. A theorem is proven which states that the iterative scheme converges to a nontrivial MHD equilbrium as long as solutions exist at each step of the iteration.

Identification of Kelvin-Helmholtz generated vortices in magnetised fluids

The Kelvin-Helmholtz Instability (KHI), arising from velocity shear across the magnetopause, plays a significant role in the viscous-like transfer of mass, momentum, and energy from the shocked solar wind into the magnetosphere. While the KHI leads to growth of surface waves and vortices, suitable detection methods for these applicable to magnetohydrodynamics (MHD) are currently lacking. A novel method is derived based on the well-established λ-family of hydrodynamic vortex identification techniques, which define a vortex as a local minimum in an adapted pressure field. The J×B Lorentz force is incorporated into this method by using an effective total pressure in MHD, including both magnetic pressure and a pressure-like part of the magnetic tension derived from a Helmholtz decomposition. The λMHD method is shown to comprise of four physical effects: vortical momentum, density gradients, fluid compressibility, and the rotational part of the magnetic tension. A local three-dimensional MHD simulation representative of near-flank magnetopause conditions (plasma β’s 0.5–5 and convective Mach numbers Mf∼0.4) under northward interplanetary magnetic field (IMF) is used to validate λMHD. Analysis shows it correlates well with hydrodynamic vortex definitions, though the level of correlation decreases with vortex evolution. Overall, vortical momentum dominates λMHD at all times. During the linear growth phase, density gradients act to oppose vortex formation. By the highly nonlinear stage, the formation of small-scale structures leads to a rising importance of the magnetic tension. Compressibility was found to be insignificant throughout. Finally, a demonstration of this method adapted to tetrahedral spacecraft observations is performed.

Impact of the Brownian motion and thermophoretic diffusion during the radiative MHD hybrid nanofluid flow past a stretching sheet

The article aims to analyze the effects of thermophoretic and Brownian motion on steady three-dimensional magnetohydrodynamics with fully developed natural convective hybrid nanofluid flow past a bidirectionally extending sheet. We assumed the water-based copper and aluminum nanoparticles suspension under the influence of the rotational effect, nonlinear chemical reaction, thermal radiations, viscous dissipation, and heat source. The flow field is modeled with the help of the basic equations. Furthermore, the problem is reduced to ordinary differential equations (ODEs) with the similarity variables. The reduced system of ODEs is solved with the semianalytical method (homotopy analysis method). The results for the state variables are displayed through graphs tables for various pertinent parameters. The thermal profile falls with the higher values of the Brownian and thermophoresis parameters, while the concentration profile shows an opposite trend with the increasing values of the Brownian parameter. Also, the slip parameter decreases both the thermal and concentration profiles as well as the surface drag. The velocity profiles along both directions fall with the higher magnetic strength and porosity parameters. The heat source and radiations parameter enhances the thermal profile with increasing values. The study also recommends the opposite trends for the axial and transverse velocities with increasing value of the stretching ratio factor. The proposed method convergence is present through [Formula: see text] curves for the regions [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] The skin friction and Nusselt number are displayed through tables numerically for various values of volume fraction and other important parameters.

The Impact of Stellar Radiative Feedback on Formation of Young Massive Clusters via Fast H i Gas Collisions

Young massive clusters (YMCs) are dense aggregates of young stars and are often speculated as potential precursors to globular clusters. However, the formation mechanism of massive and compact gas clumps that precede YMCs remains unknown. In this paper, we study the formation of such massive clumps via fast H i gas collisions (∼100 km s−1) as suggested by recent observations and their subsequent evolution into YMCs by using three-dimensional magnetohydrodynamics simulations involving self-gravity and detailed thermal/chemical processes. In particular, the impact of ionization feedback from stellar radiation is included in an approximate fashion where the temperature within the H ii regions is elevated to 10,000 K, while supernova feedback is not included. We examine whether the resulting massive clumps can survive this ionization feedback and evolve into YMCs. Our simulations reveal the emergence of gas clumps that not only possess substantial mass (∼105 M ⊙) but also sufficient compactness (∼5 pc). Notably, these clumps exhibit significantly higher escape velocities compared to the sound speed of the H ii region, indicating effective gravitational retention of gas against feedback-induced evaporation. Consequently, these conditions foster efficient star formation within the massive gas clumps, ultimately leading to their evolution into YMCs. We also perform simulations involving lower-velocity gas collisions, approximately 15 km s−1, typical shock velocities induced by galactic superbubbles. In contrast to the high-velocity collisions, we find that molecular cloud formation does not occur in the case of 1 cm−3 gas collision, while YMC formation is observed in the presence of denser gas of 10 cm−3. However, the formation of YMCs requires compression periods exceeding 10 Myr in these cases, indicating a potential preference for gas collisions driven by intergalactic interactions rather than galactic superbubbles for YMC formation.

Three-Dimensional Radiative Rotating MHD Nanofluid Flow of Over a Stretched Sheet with Homogeneous-Heterogeneous Chemical Reactions

CNTs are employed in energy storage, device modelling, automobile parts, water filters, thin-film electronics, coating, and more. The continuous three-dimensional (3D) magnetohydrodynamics (MHD) rotational flow of water-based nanofluid comprising SWCNT and MWCNT past a stretching/shrinking sheet under magnetic field and homogeneous-heterogeneous chemical processes is examined in this study. Heat transport is also examined with thermal radiation and heat source/sink. The governing partial differential equations (PDEs) are transformed to non-linear ODEs using proper similarity transformations and solved numerically using MATLAB's bvp4c package. Graphs and tables show how magnetic field, rotational, suction/injection, thermal radiation, heat source/sink parameters, nanoparticle (NP) volume fraction, and homogeneous and heterogeneous reactions affect velocity, temperature, concentration, skin friction coefficient, and Nusselt number. For larger rotational parameters, the main velocity declines and the second velocity increases, and MWCNTs flow more than SWCNTs.

The Dynamic Response of Jovian Magnetotail Reconnection to Enhanced Solar Wind Ram Pressure

In this study, we employ the Grid Agnostic Magnetohydrodynamic (MHD) for Extended Research Applications (GAMERA), a high-resolving-power, three-dimensional global MHD model, to simulate magnetotail reconnection in Jupiter's magnetosphere. While previous satellite observations have provided initial statistics on magnetotail reconnection properties at Jupiter, they have been limited in spacetime coverage, leaving the dynamic process of Jovian magnetotail reconnection and its response to the solar wind (SW) poorly understood. Using MHD simulations, we quantitatively analyze the temporal evolution and spatial dependence of nightside reconnection in Jupiter's magnetotail under ideal quiet and enhanced SW conditions. Our results demonstrate that magnetotail reconnection tends to occur in the midnight and postmidnight sectors, with a low occurrence in the premidnight sector, consistent with both Galileo and Juno observations and predictions by Delamere & Bagenal. The magnetic local time (MLT)–radial distribution of magnetotail reconnection is broad, indicating that Jovian magnetotail reconnection is always dynamic rather than steady state. Enhanced SW ram pressure can decrease the MLT coverage of magnetotail reconnection by compressing Jupiter's magnetosphere. However, the occurrence of magnetotail reconnection near the midnight and postmidnight sectors is enhanced by SW compression beyond 60 R J, but is not significantly impacted by SW compression within 60 R J. Conversely, SW compression suppresses reconnection in the premidnight sector, leading to a stronger dawn–dusk asymmetry in the occurrence and location of magnetotail reconnection. This study validates the applicability of the GAMERA code for simulating Jupiter’s magnetosphere and provides complementary insights into the dynamic structure and the SW response of Jupiter’s magnetosphere.

Cloud Dissipation and Disk Wind in the Late Phase of Star Formation

We perform a long-term simulation of star and disk formation using three-dimensional nonideal magnetohydrodynamics. The simulation starts from a prestellar cloud and proceeds through the long-term evolution of the circumstellar disk until ∼1.5 × 105 yr after protostar formation. The disk has size ≲50 au and little substructure in the main accretion phase because of the action of magnetic braking and the magnetically driven outflow to remove angular momentum. The main accretion phase ends when the outflow breaks out of the cloud, causing the envelope mass to decrease rapidly. The outflow subsequently weakens as the mass accretion rate also weakens. While the envelope-to-disk accretion continues, the disk grows gradually and develops transient spiral structures, due to gravitational instability. When the envelope-to-disk accretion ends, the disk becomes stable and reaches a size ≳300 au. In addition, about 30% of the initial cloud mass has been ejected by the outflow. A significant finding of this work is that after the envelope dissipates a revitalization of the wind occurs, and there is mass ejection from the disk surface that lasts until the end of the simulation. This mass ejection (or disk wind) is generated because the magnetic pressure significantly dominates both the ram pressure and thermal pressure above and below the disk at this stage. Using the angular momentum flux and mass-loss rate estimated from the disk wind, the disk dissipation timescale is estimated to be ∼106 yr.

Solar Eruptions in Nested Magnetic Flux Systems

The magnetic topology of erupting regions on the Sun is a key factor in the energy buildup and release, and the subsequent evolution of flares and coronal mass ejections (CMEs). The presence/absence of null points and separatrices dictates whether and where current sheets form and magnetic reconnection occurs. Numerical simulations show that energy buildup and release via reconnection in the simplest configuration with a null, the embedded bipole, is a universal mechanism for solar eruptions. Here we demonstrate that a magnetic topology with nested bipoles and two nulls can account for more complex dynamics, such as failed eruptions and CME–jet interactions. We investigate the stalled eruption of a nested configuration on 2013 July 13 in NOAA Active Region 11791, in which a small bipole is embedded within a large transequatorial pseudo-streamer containing a null. In the studied event, the inner active region erupted, ejecting a small flux rope behind a shock accompanied by a flare; the flux rope then reconnected with pseudo-streamer flux and, rather than escaping intact, mainly distorted the pseudo-streamer null into a current sheet. EUV and coronagraph images revealed a weak shock and a faint collimated outflow from the pseudo-streamer. We analyzed Solar Dynamics Observatory and Solar TErrestrial RElations Observatory observations and compared the inferred magnetic evolution and dynamics with three-dimensional magnetohydrodynamics simulations of a simplified representation of this nested fan-spine system. The results suggest that the difference between breakout reconnection at the inner null and at the outer null naturally accounts for the observed weak jet and stalled ejection. We discuss the general implications of our results for failed eruptions.

Non-uniqueness in law of three-dimensional magnetohydrodynamics system forced by random noise

Non-uniqueness in law of three-dimensional magnetohydrodynamics system forced by random noise

Asymptotic quasisymmetric high-beta three-dimensional magnetohydrodynamic equilibria near axisymmetry

Quasisymmetry (QS), a hidden symmetry of the magnetic field strength, is known to support nested flux surfaces and provide superior particle confinement in stellarators. In this work, we study the ideal magnetohydrodynamic (MHD) equilibrium and stability of high-beta plasma in a large-aspect-ratio stellarator. In particular, we show that the lowest-order description of a near-axisymmetric equilibrium vastly simplifies the problem of three-dimensional quasisymmetric MHD equilibria, which can be reduced to a standard elliptic Grad–Shafranov equation for the flux function. We show that any large-aspect-ratio tokamak, deformed periodically in the vertical direction, is a stellarator with approximate volumetric QS. We discuss exact analytical solutions and numerical benchmarks. Finally, we discuss the ideal ballooning and interchange stability of some of our equilibrium configurations.

Three-Dimensional Magnetohydrodynamics Casson Fluid Flow Past a Non-Linearly Stretching Surface with Nanoparticles

This article, the three-dimensional flow of a casson fluid over a non-linearly stretching surface by bilateral directions along the xy-plane under boundary layer approximation is estimated. We have considered the the effect of magnetohydrodynamics (MHD) and the condition of natural convective over the stretching surface. Moreover, The influences of boundary condition at temperatures and nanoparticles in motion are thermophoresis, Brownian motion and radiation are considered. The method of solved equation by using the appropriate transformations, the system non-linear partial differential equations along with the boundary conditions is transformed into coupled non-linear ordinary differential equations. The numerical solutions of the mathematics formulated equations are solved by using a Runge–Kutta method with a shooting technique. The new obtained results are checked with previously published work for special cases of the problem in order to access the accuracy of numerical method and the convergency between are found to be in excellent agreement through ratified by tabular results. The emerging parameters behavior are discussed graphically in the form of velocity, temperature and fraction of nanoparticles. The number of Nusselt and number of Sherwood are calculated by numerical computations solution are expressed by tabular results. We have observed that the assignment denoted by parameters characteristics have significant effect on flow, transfer of heat and mass. Generally, The results are expressed by graphically, in tabular form and the physical aspects of the problem are determined.